We provide here an example data set (subject WK), described in Drucker, Kerr & Aguirre (2009). This subject was scanned while viewing a continuous presentation of two-dimensional shapes, drawn from a di-octagonal arrangement of stimuli defined by a two-dimensional stimulus space:

Iterative behavioral testing and stimulus space adjustment was used to create a stimulus space which corresponds to equal and regular perceptual distances between the stimuli. The analyses that follow test for the existence of symmetric neural carry-over (adaptation) effects that are proportional to stimulus pair dissimilarity. Shown below (right) are the X and Y coordinates of the stimuli within the space, and (middle) the standard numbering within the di-octagonal grid. A dissimilarity matrix (left) visually indicates the distance between each pairing of the stimuli within the space, coded on a gray scale (black=near, white=far).

1 0.2929 0 2 0.7071 0 3 1.0000 0.2929 4 1.0000 0.7071 5 0.7071 1.0000 6 0.2929 1.0000 7 0.0000 0.7071 8 0.0000 0.2929 9 0.2929 0.2929 10 0.5000 0.2071 11 0.7071 0.2929 12 0.7929 0.5000 13 0.7071 0.7071 14 0.5000 0.7929 15 0.2929 0.7071 16 0.2071 0.5000

During scanning, the subject made a perceptual decision regarding each stimulus (whether a line was shifted to the left or the right of the center of the shape). Each stimulus was presented for 1400 msecs, with a 100 msec inter-stimulus-interval. The order of presentation of the 16 shapes (as well as a blank, “null” trial) was determined by an n=17, Type-1, Index-1 sequence. Out of the many possible T1I1 sequences of this length, one was selected that was found to have optimal Efficiency for detection of predicted release from adaptation effects produced by the transition from one stimulus to another.

To improve the Efficiency of the sequence for detection of “direct effects” (i.e., the effect of a stimulus as compared to the null-trial events), the duration of the null-trial events was doubled.

Five T1I1 sequences were concatenated to produce a full sequence of 1530 elements.

During scanning, a total of 765 EPI volumes were collected at a TR=3000 msecs. We provide below the data and covariates that were generated to analyze the effects of the stimuli. The data are provided following standard pre-processing (masking, slice acquisition correction, realignment, MNI spatial normalization). Both spatially smoothed (XX voxel FWHM kernel) and unsmoothed data are available. The data are in ANALYZE format. The volumes are numbered as XYYY, where X is the “scan” number (1-5) and YYY is the “image” number (0-152).

The normalized anatomical image (nDisplay.img) corresponding to these data is also provided.

A sub-directory contains the “REF” files used to generate covariates. Each file is a text file of 1530 elements. Several approaches may be used to generate covariates to analyze these data. The files below follow the approach described by Aguirre 2007, in which neural adaptation is modeled as modulation of the neural response around the mean response to all stimuli as compared to a blank screen. Covariates are reference coded with respect to the null-trials and are mean centered. These covariates correspond to the predicted neural response:

For the analysis of the BOLD fMRI data, these covariates are convolved with a standard BOLD hemodynamic response function, and accompanied by several covariates of no-interest (nuisance covariates). The complete set of covariates used are contained within the COVARIATES folder and include:

Other components of the analysis included filtering the first 25 low-frequencies from the data, and modeling the 1/f noise power spectrum present in the data using the modified general linear model. “Drift correction” was applied to the data, in which a linear trend was fit to the time-series data from each voxel for each scan and removed. The data were also “mean normalized”, in which the time-series from each voxel for each scan was divided by the mean value of the time-series. This renders the data in proportion-of-change units.

The RESULTS folder contains ANALYZE format volumes corresponding to the beta value (effect size) for each of the covariates of interest, as well as the statistical t-maps for each covariate, as measured in the spatially smoothed data. Given the effective degrees of freedom of the analysis (633), a map-wise t-threshold for the smoothed data, corresponding to an alpha=0.05, is XXX.

One important violation of the model assumptions can occur when the underlying neural representation is independent for the stimulus dimensions, but its neural instantiation is not aligned with the assumed dimensional axes of the study. For example, consider an experiment designed to examine the neural representation of rectangles. The stimulus space used in the experiment consists of rectangles that vary in height and width, and the experimenter models these two parameters. It may be the case, however, that a population of neurons has independent tuning for the sum and difference of height and width, which roughly correspond to area and aspect ratio; a 45° rotation of the axes as modeled by the experimenter. In this case, one can obtain spurious loading on the Euclidean contraction covariate.

Whenever significant loading upon the Euclidean contraction covariate is obtained in an experiment, an additional test is necessary to reject the possibility of independent, but misaligned, neural populations. Post-hoc testing of the performance of the model under assumed rotations of the stimulus axes can distinguish between the independent but rotated, and the conjointly tuned cases.

This is what the degrees argument to ''writeccocov'' is for; you may generate covariates which assume a rotated space. The ROTREFs directory of the example data contains covariates assuming various rotations of the di-octagon space.

Another kind of analysis that can be performed involves modeling each individual stimulus transition (120 in total if a symmetric dimensional effect is assumed) separately, using 120 separate covariates.

A post-hoc analysis can be formed on this basis set to detect the presence of compressive non-linearities in the stimulus representations and BOLD response. This can be accomplished by directly comparing the stimulus distance and the distances implied by the BOLD fMRI signal in adaptation recovery. To do so, we consider the pure (one-dimensional) changes on each dimension, and measure them with respect to a reference stimulus. The BOLD signal change associated with ever larger transitions is obtained, and used to construct a representation of the degree of difference in BOLD signal between stimuli, related to the degree of difference in the stimuli themselves.

(See Appendix C of an example data set (subject WK), described in Drucker, Kerr & Aguirre (2009).)

NOTE: We have recently realized that this post-hoc test can also be simply executed as a one-dimensional multi-dimensional scaling (MDS) analysis of the pair values.